Suppose we have the simple linear regression model yi beta 1

Suppose we have the simple linear regression model: yi= beta 1+beta2Xi+ui Using a sample of size n = 20 observations, we obtain the OLS estimate b2 = 1.05 and its associated standard error,s. e. (b2) = 0.57. We want to test the null hypothesis, H0 : beta2 = 0 , against the alternative hypothesis: Hx : /beta2 0. What is the value of the t statistic for this test? What are the degrees of freedom for this test? What is the 5% critical value for this test? Can we reject the null hypothesis at the 5% level?

Solution

a)The value of the t test statistic for this test is:

b2/se(b2)=1.05/0.57=1.84

b)The degrees of freedom for this test is:

DF=n-2=20-2=18

c)The 5% critical value for this test is:

t(0.05,18)=plus minus 2.101

d)The test statistic t does not fall in the critical region, so failed to reject the null hypothesis at 0.05 level of significance.